Tsükloidas

Tsükloidas is a mathematical curve traced by a point on the circumference of a circle as the circle rolls along a straight line without slipping. This cycloid is a type of trochoid, a curve generated by a point attached to a circle rolling along a line. The name "cycloid" comes from the Greek words kyklos, meaning circle, and eidos, meaning form.

The shape of a cycloid is characterized by a series of arches. Each arch is formed as the rolling circle completes one full revolution. The highest point of each arch is twice the radius of the rolling circle. The curve has cusps at its lowest points, where the point on the circumference touches the straight line. The cycloid was studied by Galileo Galilei, who attempted to find its area, and later by mathematicians like Mersenne and Roberval.

A significant property of the cycloid is its tautochrone nature. This means that regardless of where a bead starts on the curve, it will take the same amount of time to reach the lowest point, assuming it moves under the influence of gravity and without friction. This property made the cycloid important in the development of mechanics and physics. The brachistochrone problem, finding the curve of fastest descent between two points, was also famously solved by Johann Bernoulli using the cycloid.